Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 31, Problem 12A
To determine
The vernier caliper measurement.
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9.7 Given the equations
0.5x₁-x2=-9.5
1.02x₁ - 2x2 = -18.8
(a) Solve graphically.
(b) Compute the determinant.
(c) On the basis of (a) and (b), what would you expect regarding
the system's condition?
(d) Solve by the elimination of unknowns.
(e) Solve again, but with a modified slightly to 0.52. Interpret
your results.
12.42 The steady-state distribution of temperature on a heated
plate can be modeled by the Laplace equation,
0=
FT T
+
200°C
25°C
25°C
T22
0°C
T₁
T21
200°C
FIGURE P12.42
75°C
75°C
00°C
If the plate is represented by a series of nodes (Fig. P12.42), cen-
tered finite-divided differences can be substituted for the second
derivatives, which results in a system of linear algebraic equations.
Use the Gauss-Seidel method to solve for the temperatures of the
nodes in Fig. P12.42.
9.22 Develop, debug, and test a program in either a high-level language or a macro
language of your choice to solve a system of equations with Gauss-Jordan elimination
without partial pivoting. Base the program on the pseudocode from Fig. 9.10. Test the
program using the same system as in Prob. 9.18. Compute the total number of flops in
your algorithm to verify Eq. 9.37.
FIGURE 9.10
Pseudocode to implement the
Gauss-Jordan algorithm with-
out partial pivoting.
SUB GaussJordan(aug, m, n, x)
DOFOR k = 1, m
d = aug(k, k)
DOFOR j = 1, n
aug(k, j) = aug(k, j)/d
END DO
DOFOR 1 = 1, m
IF 1 % K THEN
d = aug(i, k)
DOFOR j = k, n
aug(1, j)
END DO
aug(1, j) - d*aug(k, j)
END IF
END DO
END DO
DOFOR k = 1, m
x(k) = aug(k, n)
END DO
END GaussJordan
Chapter 31 Solutions
Mathematics For Machine Technology
Ch. 31 - Measure this line segment to the nearest 164.Ch. 31 - A hole has a diameter of 13.741 mm 0.002mm+0.005mm...Ch. 31 - For the measurement 74.38 mm, find (a) the degree...Ch. 31 - Express 87.6 inches as feet.Ch. 31 - If 1450 parts can be produced in 15.35 hours, how...Ch. 31 - Prob. 6ACh. 31 - Read the decimal-inch vernier caliper measurements...Ch. 31 - Read the decimal-inch vernier caliper measurements...Ch. 31 - Read the decimal-inch vernier caliper measurements...Ch. 31 - Read the decimal-inch vernier caliper measurements...
Ch. 31 - Read the decimal-inch vernier caliper measurements...Ch. 31 - Prob. 12ACh. 31 - Read the decimal-inch vernier caliper measurements...Ch. 31 - Read the decimal-inch vernier caliper measurements...Ch. 31 - Prob. 15ACh. 31 - The tables for Exercises 15 and 16 give the...Ch. 31 - In Exercises 17 and 18, refer to the following...Ch. 31 - In Exercises 17 and 18, refer to the following...Ch. 31 - The distance between the centers of two holes can...Ch. 31 - The distance between the centers of two holes can...Ch. 31 - Prob. 21ACh. 31 - Prob. 22ACh. 31 - The distance between the centers of two holes can...Ch. 31 - Read height gage measurement settings in Exercises...Ch. 31 - Read height gage measurement settings in Exercises...Ch. 31 - The hole locations of the block in Figure 31-11...
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